LEADER 01835oam 2200241z- 450 001 9910158891603321 005 20230913112557.0 010 $a1-68195-204-1 035 $a(CKB)3710000001011781 035 $a(BIP)052212422 035 $a(EXLCZ)993710000001011781 100 $a20190218c2015uuuu -u- - 101 0 $aeng 200 10$aPersonal Reflections of Joan of Arc 210 $cXist Classics 215 $a1 online resource (193 p.) 330 8 $aThe Biography of the Greatest French Heroine "One day, riding along, we were talking about Joan's great talents, and he said, 'But, greatest of all her gifts, she has the seeing eye.' I said, like an unthinking fool, 'The seeing eye?--I shouldn't count on that for much--I suppose we all have it.' 'No,' he said; 'very few have it.' Then he explained, and made his meaning clear. He said the common eye sees only the outside of things, and judges by that, but the seeing eye pierces through and reads the heart and the soul, finding there capacities which the outside didn't indicate or promise, and which the other kind of eye couldn't detect." - Mark Twain, Personal Recollections of Joan Of Arc After the death of his family at just five years of age, Louis de Conte is sent to a small village to live with a priest. There she meets Joan of Arc, a young peasant girl who would change French history forever. Enchanted by Joan, Louis de Conte becomes her servant and also her biographer. Xist Publishing is a digital-first publisher. Xist Publishing creates books for the touchscreen generation and is dedicated to helping everyone develop a lifetime love of reading, no matter what form it takes 610 $aFiction 700 $aTwain$b Mark$027404 906 $aBOOK 912 $a9910158891603321 996 $aPersonal Reflections of Joan of Arc$93591980 997 $aUNINA LEADER 05434nam 22005295 450 001 9910971116803321 005 20250730110321.0 010 $a1-4612-1534-X 024 7 $a10.1007/978-1-4612-1534-9 035 $a(CKB)3400000000089589 035 $a(SSID)ssj0000808068 035 $a(PQKBManifestationID)11443631 035 $a(PQKBTitleCode)TC0000808068 035 $a(PQKBWorkID)10775590 035 $a(PQKB)11513692 035 $a(DE-He213)978-1-4612-1534-9 035 $a(MiAaPQ)EBC3076160 035 $a(PPN)237996499 035 $a(EXLCZ)993400000000089589 100 $a20121227d1999 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aProblems and Solutions for Complex Analysis /$fby Rami Shakarchi 205 $a1st ed. 1999. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1999. 215 $a1 online resource (XI, 246 p. 17 illus.) 300 $a"With 46 illustrations." 311 08$a0-387-98831-9 327 $aI Complex Numbers and Functions -- I.1 Definition -- I.2 Polar Form -- I.3 Complex Valued Functions -- I.4 Limits and Compact Sets -- I.6 The Cauchy-Riemann Equations -- II Power Series -- II.1 Formal Power Series -- II.2 Convergent Power Series -- II.3 Relations Between Formal and Convergent Series -- II.4 Analytic Functions -- II.5 Differentiation of Power Series -- II.6 The Inverse and Open Mapping Theorems -- III Cauchy?s Theorem, First Part -- III.1 Holomorphic Functions on Connected Sets -- III.2 Integrals over Paths -- III.5 The Homotopy Form of Cauchy?s Theorem -- III.6 Existence of Global Primitives Definition of the Logarithm -- III.7 The Local Cauchy Formula -- IV Winding Numbers and Cauchy?s Theorem -- IV.2 The Global Cauchy Theorem -- V Applications of Cauchy?s Integral Formula -- V.1 Uniform Limits of Analytic Functions -- V.2 Laurent Series -- V.3 Isolated Singularities -- VI Calculus of Residues -- VI.1 The Residue Formula -- VI.2 Evaluation of Definite Integrals -- VII Conformal Mappings -- VII.2 Analytic Automorphisms of the Disc -- VII.3 The Upper Half Plane -- VII.4 Other Examples -- VII.5 Fractional Linear Transformations -- VIII Harmonic Functions -- VIII.1 Definition -- VIII.2 Examples -- VIII.3 Basic Properties of Harmonic Functions -- VIII.4 The Poisson Formula -- VIII.5 Construction of Harmonic Functions -- IX Schwarz Reflection -- IX.2 Reflection Across Analytic Arcs -- X The Riemann Mapping Theorema -- X.1 Statement of the Theorem -- X.2 Compact Sets in Function Spaces -- XI Analytic Continuation along Curves -- XI.1 Continuation Along a Curve -- XI.2 The Dilogarithm -- XII Applications of the Maximum Modulus Principle and Jensen?s Formula -- XII.1 Jensen?s Formula -- XII.2 The Picard-Borel Theorem -- XII.6 The Phragmen-Lindelof and Hadamard Theorems -- XIII Entire and MeromorphicFunctions -- XIII.1 Infinite Products -- XIII.2 Weierstrass Products -- XIII.3 Functions of Finite Order -- XIII.4 Meromorphic Functions, Mittag-Leffler Theorem -- XV The Gamma and Zeta Functions -- XV.1 The Differentiation Lemma -- XV.2 The Gamma Function -- XV.3 The Lerch Formula -- XV.4 Zeta Functions -- XVI The Prime Number Theorem -- XVI.1 Basic Analytic Properties of the Zeta Function -- XVI.2 The Main Lemma and its Application. 330 $aThis book contains all the exercises and solutions of Serge Lang's Complex Analy­ sis. Chapters I through VITI of Lang's book contain the material of an introductory course at the undergraduate level and the reader will find exercises in all of the fol­ lowing topics: power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings and har­ monic functions. Chapters IX through XVI, which are suitable for a more advanced course at the graduate level, offer exercises in the following subjects: Schwarz re­ flection, analytic continuation, Jensen's formula, the Phragmen-LindelOf theorem, entire functions, Weierstrass products and meromorphic functions, the Gamma function and the Zeta function. This solutions manual offers a large number of worked out exercises of varying difficulty. I thank Serge Lang for teaching me complex analysis with so much enthusiasm and passion, and for giving me the opportunity to work on this answer book. Without his patience and help, this project would be far from complete. I thank my brother Karim for always being an infinite source of inspiration and wisdom. Finally, I want to thank Mark McKee for his help on some problems and Jennifer Baltzell for the many years of support, friendship and complicity. Rami Shakarchi Princeton, New Jersey 1999 Contents Preface vii I Complex Numbers and Functions 1 1. 1 Definition . . . . . . . . . . 1 1. 2 Polar Form . . . . . . . . . 3 1. 3 Complex Valued Functions . 8 1. 4 Limits and Compact Sets . . 9 1. 6 The Cauchy-Riemann Equations . 606 $aMathematical analysis 606 $aAnalysis 615 0$aMathematical analysis. 615 14$aAnalysis. 676 $a515/.9 700 $aShakarchi$b Rami$4aut$4http://id.loc.gov/vocabulary/relators/aut$061671 701 $aLang$b Serge$f1927-2005.$01160 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910971116803321 996 $aProblems and Solutions for Complex Analysis$94412596 997 $aUNINA